The present invention relates to sports devices which include a shaft or rod in its construction, particularly sports devices where the shaft is moved at high speeds through the air.
Many sports devices incorporate a shaft or rod in their construction. Some examples include golf clubs, baseball bats, fishing poles, ski poles, rackets (such as a tennis racket), lacrosse sticks, bicycle frames, and rowing oars. In use, these shafts are typically moved through a fluid such as air or water, and it is generally desirable to move these shafts at high speeds. One method of increasing the speed at which a shaft moves through the air is to increase the force applied to the shaft. Another method of increasing the shaft speed is to decrease the forces, including fluid resistance, that counter the shaft movement.
As explained in Fundamentals of Fluid Mechanics by Philip M. Gerhart and Richard J. Gross (copyright (copyright) 1985 by Addison-Wesley Publishing Co.), moving a shaft, such as a golf club shaft, through a fluid such as air causes air to flow around the shaft. If viscous forces are minimal, the air flow pattern and pressure distribution are generally symmetrical about the midplane of the shaft. If, however, viscous forces are taken into account, the analysis of the air flow becomes quite different. There is a region, i.e., the boundary layer, that develops at the surface of the shaft where the velocity of the fluid increases from zero to the free-stream value. There are significant shear stresses in the boundary layer fluid, even if the viscosity is small. The flow outside the boundary layer is determined by a balance between pressure force and fluid momentum. On the front or upstream of the shaft, the fluid momentum increases and the pressure drops while on the back side or downstream of the shaft, the fluid exchanges momentum for increasing pressure. In the boundary layer, on the other hand, the flow is determined by a balance between momentum and pressure in addition to viscous forces. Because of viscosity, the fluid inside the boundary layer has less momentum than the fluid outside the boundary layer. As the pressure begins to rise, it is necessary for the fluid back stream of the shaft to exchange momentum for pressure. Since the boundary layer is deficient in momentum, it is unable to penetrate very far into the rising pressure. The pressure causes the fluid in the boundary layer to stop and, ultimately, reverse direction. The boundary layer then separates from the shaft surface at a separation point and a broad wake is formed behind the shaft. The separating boundary layer pushes the flow streamlines outward and so alters the entire flow pattern and pressure distribution. The pressure on the rear of the shaft, in the wake, is low and approximately constant. The pressure on the front of the shaft is high, so there is a net pressure force (form drag) on the shaft. The shear stress on the shaft surface produces friction drag. The drag coefficient is a dimensionless parameter, which may be derived by dividing the drag force by the following:
xc2xd*xcfx81*V2*12.
At Reynolds numbers (i.e., Re=(xcfx81*V*1)/(xcexc), another dimensionless parameter typically used to decide whether flow is laminar or turbulent) greater than about 50, vortices are shed from the shaft downstream of the shaft. These vortices are shed alternately from the top and the bottom of the shaft with a definite frequency. The vortices trail behind the shaft in two rows called a Karman""s vortex street. The oscillating streamline pattern caused by the alternate vortex shedding causes a fluctuating pressure force on the shaft and hence a time-varying load. The frequency of the fluctuating force is equal to the frequency of the vortex shedding. The frequency of vortex shedding is governed by the Strouhal number (S), which may be derived by the following formula:
(xcfx89*1)/V.
Thus, when the shaft is moved or swung at a high speed, the pressures on the shaft make it difficult to move the shaft along a straight path. This is a particularly troublesome problem for golfers who are trying to squarely hit a golf ball. Similar problems are encountered with other sports devices, such as baseball bats, fishing poles, and tennis rackets. Thus, there is a need for a sports shaft or rod that is more aerodynamic and does not exhibit these problems.
The present invention satisfies this need by providing a shaft or rod with improved stability and decreased resistance, which will ultimately improve the performance of the user. The construction of the shaft of the present invention effectively lowers the coefficient of drag acting on the shaft and reduces the effect of Karman""s vortex street.
The present invention relates to a shaft adapted to move through a fluid, wherein the shaft has at least two longitudinal raised surface ridges extending along at least a portion of the length of the shaft, such that fluid resistance encountered by the shaft as it is moved through the fluid is reduced.
Preferably, the shaft has a generally circular cross-sectional area and diameter; a leading edge on the surface of the shaft along the length of the shaft, which generally leads the shaft""s movement through the fluid; and at least two ridges located on the surface of the shaft along at least a portion of the length of the shaft, wherein the at least two ridges are located less than 180xc2x0 apart and at least 90xc2x0 from the leading edge of the shaft.
The present invention also relates to a shaft which is incorporated into various sports devices. The shaft of the present invention includes ridges, wherein the cross sectional area of the ridges are small compared to the cross sectional area of the shaft itself. This shape reduces fluid resistance and stabilizes the shaft while in motion, thereby improving the performance of the sports device. Reducing the resistance is accomplished by improving the distribution of air pressure along the shaft surface due to the presence and location of the ridges. The use of this novel shaft is contemplated for various sports devices such as a golf club, a fishing pole, a baseball bat, a ski pole, a tennis racket, a lacrosse stick, a bicycle frame, or a rowing oar.